2.6 KiB
2.6 KiB
title | id | challengeType |
---|---|---|
Entropy | 599d15309e88c813a40baf58 | 5 |
Description
Calculate the Shannon entropy H of a given input string.
Given the discreet random variable $X$ that is a string of $N$ "symbols" (total characters) consisting of $n$ different characters (n=2 for binary), the Shannon entropy of X in bits/symbol is :
$H_2(X) = -\sum_{i=1}^n \frac{count_i}{N} \log_2 \left(\frac{count_i}{N}\right)$
where $count_i$ is the count of character $n_i$.
Instructions
Tests
tests:
- text: <code>entropy</code> is a function.
testString: assert(typeof entropy === 'function', '<code>entropy</code> is a function.');
- text: <code>entropy("0")</code> should return <code>0</code>
testString: assert.equal(entropy('0'), 0, '<code>entropy("0")</code> should return <code>0</code>');
- text: <code>entropy("01")</code> should return <code>1</code>
testString: assert.equal(entropy('01'), 1, '<code>entropy("01")</code> should return <code>1</code>');
- text: <code>entropy("0123")</code> should return <code>2</code>
testString: assert.equal(entropy('0123'), 2, '<code>entropy("0123")</code> should return <code>2</code>');
- text: <code>entropy("01234567")</code> should return <code>3</code>
testString: assert.equal(entropy('01234567'), 3, '<code>entropy("01234567")</code> should return <code>3</code>');
- text: <code>entropy("0123456789abcdef")</code> should return <code>4</code>
testString: assert.equal(entropy('0123456789abcdef'), 4, '<code>entropy("0123456789abcdef")</code> should return <code>4</code>');
- text: <code>entropy("1223334444")</code> should return <code>1.8464393446710154</code>
testString: assert.equal(entropy('1223334444'), 1.8464393446710154, '<code>entropy("1223334444")</code> should return <code>1.8464393446710154</code>');
Challenge Seed
function entropy (s) {
// Good luck!
}
Solution
function entropy(s) {
// Create a dictionary of character frequencies and iterate over it.
function process(s, evaluator) {
let h = Object.create(null),
k;
s.split('').forEach(c => {
h[c] && h[c]++ || (h[c] = 1); });
if (evaluator) for (k in h) evaluator(k, h[k]);
return h;
}
// Measure the entropy of a string in bits per symbol.
let sum = 0,
len = s.length;
process(s, (k, f) => {
const p = f / len;
sum -= p * Math.log(p) / Math.log(2);
});
return sum;
}